引力向量及梯度张量在坐标系之间的变换

Computer-Aided Transformation of Gravity Vector and Its Gradient Tensor Between Coordinate Systems

引力向量和引力梯度张量在局部和全局坐标系间的转换过程是对卫星重力梯度测量进行模拟研究的主要手段和重要步骤。提出了利用计算机符号运算辅助推导该转换过程的新思想。首先通过对该过程进行分析,指出其运算繁琐复杂;然后通过对理论推导过程的分解,确定了引力向量和引力梯度张量在局部和全局坐标系之间转换的各关键步骤;并借助于计算机符号运算实现了这一转换过程的计算机推演,成功地得到了完整的符号公式结果。所编写的符号推演程序在多台计算机的多种平台上获得了一致的结果。实验结果表明,计算机符号运算对于公式体系繁杂的卫星重力学理论研究来说具有极大的增效作用。

Aiming at the implementation of transformation of gravity vector as well as its gradient tensor between local and global coordinate systems a novel method was proposed which took advantage of computer symbolic operation in conventional derivation. Analysis of the trarisformation process showed that though characterized by complex and complicated operation, it was still one key process for the sirhulation research of satellite gravity gradient survey Therefore the conventional theoretical derivation of the transformation of the gravity vector and its gradient tensor between local and global coordinate systems was firstly analyzed and taken apart, and then with the aid of computer symbolic operation, the derivation of the process was also completed on computer. The symbolic operation program had been tested on different computer platforms and consistent result had also been acquired. Results indicate that the symbolic operation wais a helpful efficiency-amplifier for satellite gravity research that was characterized by a complicated formula system.